How to call Athena Rest APIs

Have you looked at the following documentation - https://docs.aws.amazon.com/athena/latest/APIReference/API_Operations.html

It has the list of APIs along with sample requests, responses and errors.

It also gives you sample code in different programming languages.

If you have already looked at this documentation but still run into problems understanding the APIs, then I would recommend opening Support tickets with specific details about which APIs do not work.